Circuit board (technical elements) with particles
Animation Nodes can be used here. First, read my answer here to create the trace visualization. Then, we are going to alter the node tree to limit the computed directions to multiples of 45 degrees. To do that, the Snap Vector operator would be used. Take the following node tree for example:



The snap operator snaps the vector to the nearest point in a grid with uniform spacing, the spacing is defined by the snap vector. Since the origin point of the space is also a possible point for snapping, and since we don't want to snap to it, we normalize the vector first, consequently, the vector will never be closer to the origin, except for the case of a zero vector, which is practically impossible to happen in a curl field, so we don't have to worry about it.

Now, all you have to do is quantize the output vector of the curl subprogram using the snap node as shown above.